• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.25-43
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• 2005

Let F be a finite field of prime power order q(odd) and the multiplicative order of q modulo $2^{n}\;(n>1)\;be\; {\phi}(2^{n})/2$. If n > 3, then q is odd number(prime or prime power) of the form $8m{\pm}3$. If q = 8m - 3, then the ring $R_{2^n} = F[x]/ < x^{2^n}-1 >$ has 2n primitive idempotents. The explicit expressions for these primitive idempotents are obtained and the minimal QR cyclic codes of length $2^{n}$ generated by these idempotents are completely described. If q = 8m + 3 then the expressions for the 2n - 1 primitive idempotents of $R_{2^n}$ are obtained. The generating polynomials and the upper bounds of the minimum distance of minimal QR cyclic codes generated by these 2n-1 idempotents are also obtained. The case n = 2,3 is dealt separately.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.919-947
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• 2009

In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C($-2n_1$, $2n_2$, $-2n_3$, ..., $(-1)_r2n_r$) in terms of $n_1$, $n_2$, ..., $n_r$. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link $L^{(3)}$ with rational quotient L = C(2, $n_1$, -2, $n_2$, ..., $n_r$, $(-1)^r2$) for any nonzero integers $n_1$, $n_2$, ..., $n_r$ and give a formula for the span of the Jones polynomial of $L^{(3)}$ in terms of $n_1$, $n_2$, ..., $n_r$ with $n_i{\neq}{\pm}1$ for all i=1, 2, ..., r.

• YAKHAK HOEJI
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• v.33 no.4
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• pp.246-252
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• 1989

2-Amino-1-N-methyl benzamide, 2-N-benzyl amino benzamide, 2-N-phenyl amino benzamide of 2-amino benzamide derivatives were reacted with ${\alpha}-bromo$ acetaldehyde diethyl acetal in basic condition. 2-N-alkylated products were prepared from 2-amino-1-N-methyl benzamide and 2-N-phenyl amino benzamide. 1-N-benzyl-1.4-benzodiazepin-5-one was prerpared from 2-N-benzyl aminobenzamide via intramolecular cyclization. However, 2-amino-1-N-methyl benzamide with sodium amide did not react to 1.4-benzodiazepin-5-one derivative but 3-methyl-quinazoline-2.4-dione was obtained.

• Journal of IKEEE
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• v.24 no.4
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• pp.1117-1121
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• 2020

In this work, it was confirmed that a SnO2 catalyst deposited by an atomic layer deposition(ALD) process can be employed in AlGaN/GaN heterostructure FET to detect NO2 gas. The fabricated HFET sensors on AlGaN/GaN-on-Si platform demonstrated that the devices with or without n-situ SiN have sensitivity of 5.5 % and 38 % at 200 ℃, respectively with response to 100 ppm-NO2.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.707-719
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• 2020

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n + 1)-dimensional Sasakian manifold admits a weakly Einstein metric, then its scalar curvature s satisfies -6 ⩽ s ⩽ 6 for n = 1 and -2n(2n + 1) ${\frac{4n^2-4n+3}{4n^2-4n-1}}$ ⩽ s ⩽ 2n(2n + 1) for n ⩾ 2. Secondly, for a (2n + 1)-dimensional weakly Einstein contact metric (κ, μ)-manifold with κ < 1, we prove that it is flat or is locally isomorphic to the Lie group SU(2), SL(2), or E(1, 1) for n = 1 and that for n ⩾ 2 there are no weakly Einstein metrics on contact metric (κ, μ)-manifolds with 0 < κ < 1. For κ < 0, we get a classification of weakly Einstein contact metric (κ, μ)-manifolds. Finally, it is proved that a weakly Einstein almost cosymplectic (κ, μ)-manifold with κ < 0 is locally isomorphic to a solvable non-nilpotent Lie group.

• Journal of Powder Materials
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• v.11 no.4
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• pp.294-300
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• 2004

This study for preparation of aluminum nitride (AlN) with high purity was carried out by self-propagating high-temperature synthesis method in two different systems, $Al-N_{2}$ and $Al-N_{2}$-AlN, with the change of nitrogen gas pressure and dilution factor. On the occasion of $Al-N_{2}$ system, unreacted aluminum was detected in the product in spite of high nitrogen pressure, 10 MPa, This may be caused by obstructing nitrogen gas flow to inner part of molten and agglomerate of aluminum, formed in pre-heating zone. In $Al-N_{2}$-AlN system, AlN with a purity of 95% or ever can be prepared in the condition of $f_{Dil}\geq0.5$, $P_{N_{2}}\geq$ 1 MPa, and the purity can be elevated to 98% over in the condition of $f_{Dil}$ = 0.7 and $P_{N_{2}}$ = 10 MPa.

• Journal of the Korean Ceramic Society
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• v.32 no.7
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• pp.809-816
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• 1995

Ti1-xAlxN films were successfully deposited on high speed steel and silicon wafer by plasma-assisted chemical vapor deposition using a TiCl4/AlCl3/N2/Ar/H2 gas mixture. Plasma process enabled N2 gas to nitride AlCl3, which is not possible in sense of thermodynamics. XPS analyses revealed that the deposited layer contained Al-N bond as well as Ti-N bond. Ti1-xAlxN films were polycrystalline and had single phase, B1-NaCl structure of TiN. Interplanar distance, d200, of (200) crystal plane of Ti1-xAlxN was, however, decreased with Al content, x. Al incorporation into TiN caused the grain size to be finer and changed strong (200) preferred orientation of TiN to random oriented microstructure. Those microstructural changes with Al addition resulted in the increase of micro-hardness of Ti1-xAlxN film up to 2800Kg/$\textrm{mm}^2$ compared with 1400Kg/$\textrm{mm}^2$ of TiN.

• Journal of the Korean Chemical Society
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• v.53 no.3
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• pp.272-278
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• 2009

The optimized structures and vibrational frequencies for $Ca^+-(CO)_n$ and $Ca^+-(CO_2)_n$ (n=1,2) complexes were calculated with MP2 and B3LYP methods employing 6-311++G(2d,p) basis sets. Also the binding energies were investigated for all complexes to compare the stabilities. For $Ca^+-(CO)_n$ C-bonded complexes are more stable than O-bonded complexes. Two stable conformations, linear and $C_{2v}$ form, are possible for $Ca^+-(CO)_2$ complexes and the $C_{2v}$ form is more stable than the linear form. $Ca^+-(CO_2)_2$ also has two possible conformations and linear form has slightly lower energy than $C_{2v}$ form.

• Clean Technology
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• v.17 no.2
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• pp.134-141
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• 2011

The effects of the compounds and concentrations of nitrogenous electron acceptor, the ratio of electron donor/electron acceptor (C/N), and the complexity of electron donor on the emission of $N_2O$ during wastewater denitrification were quantitatively investigated in this study. The higher ${NO_3}^-$ and ${NO_2}^-$ concentrations, the more $N_2O$ emission was observed. ${NO_2}^-$ has strong effect on $N_2O$ emission as it emitted morc $N_2O$ than ${NO_3}^-$, 50 mg/L of ${NO_2}^-$-N gave the highest conversion (9.3%) and yield (9.8%) of $N_2O$ while ${NO_3}^-$-N (50 mg/L) gave 5.6% conversion and 11.0% yield. Lower C/N ratio decreases nitrogen removal efficiency, but it increases the conversion of $N_2O$ because of the incomplete denitrification by the limited organic carbon. When real domestic wastewater is used as the electron donor of the denitrification, $N_2O$ emission is reduced to 1/10 of the emission when single carbon (acetate) is used. It is thought that multiple carbon source utilizes many denitrification pathways and it seems to be helpful for the reduction of $N_2O$ emission.